bgnbd_CET {CLVTools} R Documentation

## BG/NBD: Conditional Expected Transactions

### Description

Calculates the expected number of transactions in a given time period based on a customer's past transaction behavior and the BG/NBD model parameters.

• `bgnbd_nocov_CET` Conditional Expected Transactions without covariates

• `bgnbd_staticcov_CET` Conditional Expected Transactions with static covariates

### Usage

```bgnbd_nocov_CET(r, alpha, a, b, dPeriods, vX, vT_x, vT_cal)

bgnbd_staticcov_CET(
r,
alpha,
a,
b,
dPeriods,
vX,
vT_x,
vT_cal,
vCovParams_trans,
vCovParams_life,
mCov_trans,
mCov_life
)
```

### Arguments

 `r` shape parameter of the Gamma distribution of the purchase process `alpha` scale parameter of the Gamma distribution of the purchase process `a` shape parameter of the Beta distribution of the lifetime process `b` shape parameter of the Beta distribution of the lifetime process `dPeriods` number of periods to predict `vX` Frequency vector of length n counting the numbers of purchases. `vT_x` Recency vector of length n. `vT_cal` Vector of length n indicating the total number of periods of observation. `vCovParams_trans` Vector of estimated parameters for the transaction covariates. `vCovParams_life` Vector of estimated parameters for the lifetime covariates. `mCov_trans` Matrix containing the covariates data affecting the transaction process. One column for each covariate. `mCov_life` Matrix containing the covariates data affecting the lifetime process. One column for each covariate.

### Details

`mCov_trans` is a matrix containing the covariates data of the time-invariant covariates that affect the transaction process. Each column represents a different covariate. For every column a gamma parameter needs to added to `vCovParams_trans` at the respective position.

`mCov_life` is a matrix containing the covariates data of the time-invariant covariates that affect the lifetime process. Each column represents a different covariate. For every column a gamma parameter needs to added to `vCovParams_life` at the respective position.

### Value

Returns a vector containing the conditional expected transactions for the existing customers in the BG/NBD model.

### References

Fader PS, Hardie BGS, Lee KL (2005). ““Counting Your Customers” the Easy Way: An Alternative to the Pareto/NBD Model” Marketing Science, 24(2), 275-284.

Fader PS, Hardie BGS (2013). “Overcoming the BG/NBD Model's #NUM! Error Problem” URL http://brucehardie.com/notes/027/bgnbd_num_error.pdf.

Fader PS, Hardie BGS (2007). “Incorporating time-invariant covariates into the Pareto/NBD and BG/NBD models.” URL http://www.brucehardie.com/notes/019/time_invariant_covariates.pdf.

Fader PS, Hardie BGS, Lee KL (2007). “Creating a Fit Histogram for the BG/NBD Model” URL https://www.brucehardie.com/notes/014/bgnbd_fit_histogram.pdf

[Package CLVTools version 0.9.0 Index]